Istituto Nazionale di Ricerca Metrologica

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1 Istituto Nazionale di Ricerca Metrologica G. D Agostino (1), S. Desogus (1), A. Germak (1), C. Origlia (1), D. Quagliotti (1), G. Celli (2) and O. Francis (3) MEASUREMENTS OF THE ACCELERATION DUE TO GRAVITY AT THE GRAVITY LABORATORY OF THE NATIONAL INSTITUTE OF METROLOGICAL RESEARCH TURIN (ITALY) T.R. 33 October 2006 (1) National Institute of Metrological Research INRIM, Italy (2) European Center for Geodynamics and Seismology ECGS, Luxembourg (3) University of Luxembourg, Luxembourg Technical Report I.N.RI.M. 1

2 ABSTRACT The work hereafter described was carried out during the period October-November, 2005 by the National Institute of Metrological Research (INRIM), formerly Institute of Metrology G.Colonnetti (IMGC-CNR), and in June, 2006 by the European Center for Geodynamics and Seismology (ECGS), Luxemburg. The experimental results of the measurement of the acceleration due to gravity carried out at the Gravity Laboratory of INRIM are reported. The estimate of the absolute acceleration due to gravity together with the vertical gradient are reported. The observation site at the Gravity Laboratory of INRIM is available as a reference absolute station for a gravity net. Absolute measurements were performed by INRIM with the new transportable ballistic gravimeter, the IMGC-02. The measurement apparatus and the measurement uncertainty are shortly described. Relative measurements were performed by ECGS with the spring gravimeter Scintrex CG5#008. The measurement traceability is assured because the IMGC-02 adopts length and time standards traceable to the national standards. It participates to the International Comparisons of Absolute Gravimeters (ICAGs) organized by the Bureau International des Poids et Mesures (BIPM) to assure the declared level of uncertainty. The CG5#008 measurement scale is calibrated with another absolute gravimeter, the FG

3 CAPTIONS INDEX ABSTRACT... 2 CAPTIONS INDEX... 3 TABLES and FIGURE INDEX INTRODUCTION DESCRIPTION OF THE IMGC Measurement method Measurement apparatus MEASUREMENT UNCERTAINTY The instrumental uncertainty of the IMGC EXPERIMENTAL RESULTS INRIM observation site Measurement sessions Vertical gradient REFERENCES

4 FIGURES and TABLES INDEX Figure 1.1: The new absolute gravimeter IMGC-02 at the INRIM Gravity Laboratory. 5 Figure 1.2: The relative spring gravimeter Scintrex CG5# Figure 2.1: Schematic layout of the IMGC-02 Absolute Gravimeter... 7 Figure 2.2: GravisoftM manager front panel... 8 Figure 2.3: GravisoftPP post-processing front panel... 8 Table 3: Instrumental uncertainty of the IMGC-02 absolute gravimeter Figure 4.1: Basement-plan of the INRIM Dynamometric section and detail of the gravity laboratory with the observation point (dimensions in centimeters) Figure 4.2a: Density frequency of measurements (Oct 26, Nov 2) Figure 4.2b: Density frequency of measurements (Nov 7, 8, 10) Figure 4.2c: Density frequency of measurements (Nov 22, 23, 28) Figure 4.3: Measurement results obtained during the eight sessions Figure 4.4: Observation sessions retained for the estimate of the mean value Table 4.1: Measurement uncertainty of the IMGC-02 absolute gravimeter at INRIM Gravity Laboratory Table 4.2: Experimental results at the Gravity Laboratory of INRIM Table 4.3: Apparatus setup at the Gravity Laboratory of INRIM Figure 4.5: Gravity field along the vertical at the Gravity Laboratory of INRIM

5 1 INTRODUCTION The measurement of the local gravitational acceleration, g, has been performed with the new gravimeter IMGC-02 /1/. The apparatus (fig. 1.1) derives from that one previously realized in collaboration with the Bureau International des Poids et Mesures in Sèvres (BIPM) /2/. Several improvements characterize the IMGC-02, among them there is the complete automation of the instrument which allows to perform the measurement during the night, when the disturbance due to the environmental noise is minimum. All the measurement sessions have been recorded and stored in data files for postprocessing. If necessary, these files are delivered for future revision or checking. The software used is the GravisoftM 1.0 and GravisoftPP 1.0, developed and tested by INRIM. Figure 1.1: The new absolute gravimeter IMGC-02 at the INRIM Gravity Laboratory 5

6 The vertical gradient was estimated with gravity data acquired with the relative spring gravimeter Scintrex CG5#008 (fig. 1.2). The gradient is used to transfer the absolute gravity value from the reference height, where it is estimated, to any other height. This allows either to compare the results obtained with instruments measuring at different heights and to transfer the absolute gravity value to the height of the sensor of a relative gravimeter which can be used to transfer the measurement outside the Laboratory. Figure 1.2: The relative spring gravimeter Scintrex CG5#008 2 DESCRIPTION OF THE IMGC MEASUREMENT METHOD The acceleration due to gravity is measured by tracking the vertical trajectory of a testmass which is thrown up in vacuum. The IMGC-02 absoulte gravimeter adopts the symmetric rise and falling method, where both the rise and falling trajectory of the testmass is recorded. The trajectory reconstruction is performed by an optical interferometer. The raw data consists in an array where each element represents the time correspondent to the passage through equally spaced levels (or stations). An equation of motion is fitted to the raw data in a total least-squares adjustment. One of the estimating parameters is the acceleration experienced by the test-mass during its flight. A measurement session consists of about 2000 launches. To assure the estimated measurement uncertainty, the g value is obtained by averaging those launches which fulfill accepting criteria. 2.2 MEASUREMENT APPARATUS A schematic layout of the apparatus is showed in fig The basic parts of the instrument are a Mach-Zehnder interferometer /3/ and a long-period (about 25 s) seismometer. The radiation of a stabilised He-Ne laser is used as the length standard. 6

7 The inertial mass of the seismometer supports a cube-corner reflector, which is the reference mirror of the interferometer. The moving mirror of the interferometer is also a cube-corner retro-reflector and is directly subjected to the free falling motion. It is thrown upwards vertically by means of a launch pad in a vacuum chamber (about Pa). A number of interference fringes emerging from the interferometer are detected by a photo-multiplier. The output signal is sampled by a high speed waveform digitizer synchronized to a Rb oscillator, used as the time standard. Equidistant stations are selected by counting a constant integer number of interference fringes (at present 1024); in particular consecutive stations are separated by a distance d = 1024 λ/2, being λ the wavelength of the laser radiation. The so called local fit method is used to time the interference signal /4/. In particular the time is computed by fitting the equation model of the interference of monochromatic waves to the interference fringe which corresponds to the selected station. As already mentioned, the space-time coordinates are processed in a least-squares algorithm, where a suitable equation model is fitted to the measured trajectory. Each throw gives an estimated g value. A personal computer runs the measurement. The pad launch is triggered only if the apparatus is found to be ready. In particular the software checks the pad launch state (loaded or unloaded), the laser state (locked or unlocked). Environmental parameters such as the local barometric pressure and the temperature are acquired each launch. seismometer interferometer photo-detector frame laser launch chamber computer electronics Figure 2.1: Schematic layout of the IMGC-02 Absolute Gravimeter The software used includes (i) the manager GravisoftM 1.0 (fig. 2.2) for driving the instrument and storing the measurement data and (ii) the post-processing GravisoftPP 1.0 (fig. 2.3) for elaborating the data-files. These programs were developed and tested on the LabVIEW7.0 platform. Geophysical corrections are applied: (i) the Earth tides and Ocean loading are computed with the ETGTAB, version 3.0, which uses the tidal potential development of 7

8 Cartwright-Tayler-Edden (1973), (ii) the polar motion correction is computed starting from the daily pole coordinates x and y (rad) obtained from the International Earth Rotation Service (IERS). The measured gravity is normalized to a nominal pressure, taking into account a barometric factor f B = m s -2 mbar -1, as recommended by the IAG 1983 resolution n.9. Instrumental corrections are also applied: (i) the diffraction correction and the (ii) laser beam verticality. The g value associated to every measurement station is estimated as mean value of n measurements carried out (after applying the above mentioned corrections) and it is reported to a specific height from the floor surface. The expanded uncertainty of the g value is also given, according to the method of combination of uncertainties suggested by the ISO GUM guide /5/. Figure 2.2: GravisoftM manager front panel Figure 2.3: GravisoftPP post-processing front panel 8

9 3 MEASUREMENT UNCERTAINTY The uncertainty associated to the g measurement is calculated combining the contributions of uncertainty of the IMGC-02 absolute gravimeter, called the instrumental uncertainty to the contribution of uncertainty depending from the observation site. 3.1 THE INSTRUMENTAL UNCERTAINTY OF THE IMGC-02 It has to be underlined that it is possible that some unrecognized effect is not present in the current measurement uncertainty budget. For this reason the uncertainty assessment can be subjected to future revision. Influence factors which are characteristic of the instrument are: vacuum level, nonuniform magnetic field, temperature gradient, electrostatic attraction, mass distribution, laser beam verticality, air gap modulation, length standard, time standard, retro-reflector balancing, radiation pressure and reference height. Tab. 3 reports the quantitative assessment of the effect of every disturbing factor. The expanded uncertainty at the 95% confidence level (coverage factor k = 2.10 and 19 degrees of freedom) is estimated to be U = m s -2. The measurement uncertainty results from the combination of the instrument uncertainty with influence factors that are dependent from the observation site: Coriolis force, floor recoil and geophysical effects such as local barometric pressure, gravity tides, ocean loading and polar motion. Uncertainty tables, related to the observation site, are attached to the experimental results below described. 9

10 CoInfluence parameters, x i Value Unit u i or a i Type A, s i Type B, a i recti g ontype of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, ν i Equivalent standard uncertainty Drag effect negligible Outgassing effect negligible Non-uniform magnetic field effect negligible Temperature gradient effect m s -2 ±1.5E E-09 U 1.1E E E E-09 Effect for Electrostatic negligible Mass distribution effect m s -2 ±5.0E E-09 rectangular 8.3E E E E-09 Laser beam verticality correction 6.6E-09 m s -2 ±2.1E E E-09 rectangular 1.5E E E E-09 Air gap modulation effect negligible Laser accuracy effect m s E E E E E E-09 Index of refraction effect negligible Beam divergence correction 1.14E-07 m s E E E E E E E-08 Beam share effect unknown unknown Clock effect m s E E-09 rectangular 3.6E E E E-09 Finges timing effect negligible Finite value of speed of light effect negligible Retroreflector balancing 0.0E+00 m ±1.0E E-04 rectangular 3.3E E E E-08 Radiation Pressure effect negligible Reference height 5.2E-01 m ±5.0E E-04 rectangular 8.3E E E E E-07 m s -2 Variance 1.5E-15-4 m 2 s Combined standard uncertainty, u 3.8E-08 m s -2 Degrees of freedom, ν eff (Welch-Satterthwaite formula) Confidence level, p Coverage factor, k (calculated with t-student) Expanded uncertainty, U = ku Relative expanded uncertainty, U rel = U/g Table 3: Instrumental uncertainty of the IMGC-02 absolute gravimeter 19 95% E-08 m s E-09 10

11 4 EXPERIMENTAL RESULTS The experimental results here reported are from measurements performed at the INRIM Gravity Laboratory during the period October-November, The data are from observations in which no identifiable instrumental problems were present. Moreover the instrumental and geophysical biases are removed and some rejecting criteria are applied to eliminate possible outliers. 4.1 INRIM OBSERVATION SITE The observation site is located on the laboratory at the basement of the Dynamometric section of INRIM /6/. The position of the measurement point, referred to the room coordinates, is showed on the plan of the building (fig. 5.1). The temperature inside the room is stabilized better than ±0.5 C. The geographic coordinates are N latitude, E longitude, and elevation 236 m. A granite block (80 80 cm) is lodged at the top of a concrete pillar which is positioned inside a concrete isolated bathtub. The pillar has a volume of about 2.5 m 3 and a mass of about 5000 kg. Moreover a layer of sand insulates the pillar from the ground Figure 4.1: Basement-plan of the INRIM Dynamometric section and detail of the gravity laboratory with the observation point (dimensions in centimeters) 11

12 4.2 MEASUREMENT SESSIONS The measurement survey consisted of eight measurement sessions. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-mass. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of fringe visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the measured g value. The final gravity value is obtained by averaging the retained trajectories. The density frequency graphs for each observation session are showed in fig. 4.2a-b-c. density frequency / 10 4 m -1 s date: 26 Oct g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = (g - g m ) 10-8 m s -2 density frequency / 10 4 m -1 s g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = 573 date: 2 Nov (g - g m ) 10-8 m s -2 Figure 4.2a: Density frequency of measurements (Oct 26, Nov 2) 12

13 density frequency / 10 4 m -1 s g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = 600 date: 7 Nov (g - g m ) 10-8 m s -2 density frequency / 10 4 m -1 s g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = 641 date: 8 Nov (g - g m ) 10-8 m s -2 density frequency / 10 4 m -1 s g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = 369 date: 10 Nov (g - g m ) 10-8 m s -2 Figure 4.2b: Density frequency of measurements (Nov 7, 8, 10) 13

14 density frequency / 10 4 m -1 s g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = 320 date: 22 Nov (g - g m ) 10-8 m s -2 density frequency / 10 4 m -1 s g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = 487 date: 23 Nov (g - g m ) 10-8 m s -2 density frequency / 10 4 m -1 s g m = ms -2 s(g) = ms -2 s(g m ) = ms -2 n = 352 date: 28 Nov (g - g m ) 10-8 m s -2 Figure 4.2c: Density frequency of measurements (Nov 22, 23, 28) 14

15 The time series are reported in fig They give an idea of the measurement reproducibility achievable with the IMGC-02 at the INRIM Gravity Laboratory. The error bars represent the expanded uncertainty of the measurement U (p = 95%). They are computed by removing from the budget influence parameters that can t change during an observation period (distribution of instrumental masses, beam divergence and retroreflector balancing) g µgal Oct 2 Nov 7 Nov 8 Nov Figure 4.3: Measurement results obtained during the eight sessions 10 Nov 22 Nov 23 Nov 28 Nov The result obtained on November, 7 is an outlyer (Chauvenet criterion), therefore it is removed from the population. The final results are reported in fig g / m s Oct 2 Nov 8 Nov Figure 4.4: Observation sessions retained for the estimate of the mean value 10 Nov 22 Nov 23 Nov 28 Nov Thep measurement uncertainty budget (tab. 4.1) includes the instrumental uncertainty reported in tab Finally tab reports the most important experimental results. Other information concerning the apparatus setup is reported on tab

16 Sensitivity Contribution to the Degrees of Equivalent Influence parameters, Type A, Type B, Type of Equivalent coefficients variance Value Unit u x i or a i freedom, i s i a i g distribution variance g standard c i = u i ( g ) = c i u ( x i ) x ν i uncertainty i Instrument uncertainty m s E E E E E E-08 Coriolis effect m s -2 ±2,6E E-08 rectangular 2.3E E E E-08 Floor recoil effect negligible Barometric pressure correction 3E-08 m s -2 ±1,0E E E-08 rectangular 3.3E E E E-09 Tide correction 6E-07 m s E E E E E E E-09 Ocean loading correction 1E-07 m s E E E E E E E-09 Polar motion correction 3E-09 m s -3 negligible 3.0E-09 Standard deviation of the mean value m s E E E E E E-09 CorectionCorr. 7.3E-07 m s Variance u ( g ) u ( g ) 1.8E-15 m 2 s Combined standard uncertainty, u 4 Degrees of freedom, ν eff u ( y) (Welch-Satterthwaite formula) νeff Confidence level, p Coverage factor, k (calculated with t-student) Expanded uncertainty, U = ku Relative expanded uncertainty, U rel = U/g 4.2E-08 m s -2 Table 4.1: Measurement uncertainty of the IMGC-02 absolute gravimeter at INRIM Gravity Laboratory = i N i = 1 4 ui ( y) ν i 27 95% E-08 m s E-09 16

17 Observation Station: Gravity Laboratory of INRIM Dates 2005, Oct 26; Nov Geodetic longitude λ = Geodetic latitude ϕ = Topographic elevation H T = 236 m Nominal pressure at the observation site P N = mbar Measurement parameters Total measurement time T m = 129 h Observation rate m r = 120 h -1 Measurement drift m d = 0.03 (u = 0.09) 10-8 m s -2 / day Total executed throws n et = Total processed and stored throws n ps = Temperature range T = ( ) C Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction (average) g pm = m s -2 Tide and ocean loading correction (average) g tol = m s -2 Local barometric pressure correction (average) g bp = m s -2 Results Corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 3278 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, ν = 33, k = 2.04) U gm = m s -2 Vertical gradient (ECGS data) within (30 130) cm γ = (u = ) 10-8 ms -2 /mm Table 4.2: Experimental results at the Gravity Laboratory of INRIM Instrument orientation Laser body to Sud direction Fitting Model Laser modulation and resonance frequency of the inertial reference Fringe visibility threshold f vt = 10% Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength λ l = m Clock frequency f c = Hz Vertical gradient input γ = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 20 Laser modulation frequency f lm = Hz Resonance frequency of the inertial reference f ir = 22.2 Hz Instrumental height h inst = m Table 4.3: Apparatus setup at the Gravity Laboratory of INRIM 17

18 Summarizing, the estimate of the acceleration due to gravity at the INRIM Gravity Laboratory during the period October November 2005, measured with the IMGC-02 gravimeter at mm from the floor is: g = ( ± 8.7) µgal The expanded uncertainty U is computed according to the ISO-GUM, taking into account all the contributions. 4.3 VERTICAL GRADIENT The sensor height of the relative spring gravimeter Scintrex CG5#008 from its base level is mm. The vertical gradient γ was estimated by measuring the gravity variation between two levels, h 1 = mm and h 2 = mm. γ is computed by fitting the following equation model to the experimental data: g = γ h + α t + k where γ is the vertical gradient, h is the level, α is the instrumental drift, t is the acquisition time and k is the offset. 8 The estimated vertical gradient was found to be γ = (0.0006) 10 ms -2 /mm (where the number in parentheses is the standard uncertainty). The gravity value along the vertical is computed starting from the acceleration measured at the reference height of the IMGC-02 absolute gravimeter, h IMGC 02 = 517 mm: ( h) = g + γ h g IMGC where h = h h 02 IMGC 02 The relevant uncertainty is: u g = u 2 g IMGC 02 + h 2 2 u γ Fig. 4.5 reports the gravity value and its expanded uncertainty (U 95%, k =2). For convenience the g value is also referred at a level of 30 mm and 1300 mm. It is worth to underline that the use of the vertical gradient outside the measurement levels (30 mm and 1300 mm) could introduce unexpected errors. 18

19 g (h = 30 mm) = ms g IMGC-02 (h = 517 mm) = ms -2 (g - g R ) 10-8 / ms U g (95%) 10-8 / ms height / mm g (h = mm) = ms g R = ms -2 height / mm γ = (0.0006) 10-8 ms -2 / mm Figure 4.5: Gravity field along the vertical at the Gravity Laboratory of INRIM 19

20 REFERENCES [1] D Agostino,G., Development and metrological characterisation of a new transportable absolute gravimeter, PhD thesis, Polytechnic of Turin, Italy, [2] Cerutti,G., Cannizzo,L., Sakuma,A., Hostache, J., A transportable apparatus for absolute gravity measurements, In: VDI-Berichte n. 212, 1974: p. 49. [3] Germak,A., Desogus,S., Origlia,C., Interferometer for the IMGC rise-and-fall absolute gravimeter", In: Metrologia, Special issue on gravimetry, Bureau International des Poids Mesures, BIPM, Pavillon De Breteuil, F-92312, Sèvres Cedex, France, 2002, Vol. 39, Nr. 5, pp [4] D Agostino,G., Germak,A., Desogus,S., Barbato,G. A Method to Estimate the Time-Position Coordinates of a Free-Falling Test-Mass in Absolute Grvimetry, In: Metrologia Vol. 42, No. 4, pp , August [5] Guide to the Expression of Uncertainty in Measurement, BIPM, IEC, ISCC, ISO, IUPAC, IUPAP, OIML, ISO, [6] Germak,A., Description of the IMGC Gravity laboratory in Turin, Italy, In : Cahiers du Centre Européen de Géodynamique et de Séismologie, Vol. 26, International Comparison of Absolute Gravimeters in Walferdange (Luxembourg) of November 2003, Nov. 2003, Ed. by O. Francis and T. van Dam, Luxembourg, pp